A Coyote and a Rat#

A coyote notices a rat running past it, toward a bush where the rat will be safe. The rat is running with a constant velocity of \(v\_{\text{rat}} = {{ params.v_r }} \rm{m/s}\) and the coyote is at rest, \(\Delta x = {{ params.d_x }} \rm{m}\) to the left of the rat. However, at \(t=0 \rm{s}\), the coyote begins running to the right, in pursuit of the rat, with an acceleration of \(a\_{\text{coyote}} = {{ params.a_c }} \rm{m/s^2}\).

Set your reference frame to be located with the origin at the original location of the coyote and the rightward direction corresponding to the positive \(x\)-direction.

Part 1#

Write the position of the coyote as a function of time \(x\_{\text{coyote}}(t)\). Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

\(t\)

t

\(\Delta x\)

dx

\(v\_{\text{rat}}\)

vr

\(a\_{\text{coyote}}\)

ac

Answer Section#

Part 2#

Write the velocity of the coyote as a function of time \(v\_{\text{coyote}}(t)\). Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

\(t\)

t

\(\Delta x\)

dx

\(v\_{\text{rat}}\)

vr

\(a\_{\text{coyote}}\)

ac

Answer Section#

Part 3#

Write the position of the rat as a function of time \(x\_{\text{rat}}(t)\). Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

\(t\)

t

\(\Delta x\)

dx

\(v\_{\text{rat}}\)

vr

\(a\_{\text{coyote}}\)

ac

Answer Section#

Part 4#

Write the velocity of the rat as a function of time \(v\_{\text{rat}}(t)\). Do not plug in numerical values for this part.

Use the following table as a reference for each variable. Note that it may not be necessary to use every variable.

For

Use

\(t\)

t

\(\Delta x\)

dx

\(v\_{\text{rat}}\)

vr

\(a\_{\text{coyote}}\)

ac

Answer Section#

Part 5#

At what time does the coyote catch the rat \(t\_{\text{catch}}\)?

Answer Section#

Please enter in a numeric value in \(\rm{s}\).

Part 6#

At this time, what is the velocity of the coyote \(v\_{\text{coyote}}(t\_{\text{catch}})\)?

Answer Section#

Please enter in a numeric value in \(\rm{m/s}\).

Part 7#

At this time, what is the velocity of the rat \(v\_{\text{rat}}(t\_{\text{catch}})\)?

Answer Section#

Please enter in a numeric value in \(\rm{m/s}\).

Part 8#

What is the location at which the coyote will catch the rat \(x\_{\text{coyote}}(t\_{\text{catch}}) = x\_{\text{rat}}(t\_{\text{catch}})\)?

Answer Section#

Please enter in a numeric value in \(\rm{m}\).

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.